The White House(WASHINGTON) -- President Obama said an 11th-hour agreement to avert year-end tax hikes on 98 percent of Americans is "within sight" but not yet complete with just hours to go before the nation reaches the so-called fiscal cliff.

"There are still issues left to resolve but we're hopeful Congress can get it done," Obama said Monday at a White House news conference. "But it's not done."

Congressional and White House negotiators have forged the contours of an agreement that would extend current tax rates for households making $450,000 or less; raise the estate tax from 35 to 40 percent for estates larger than $5 million; and prevent the Alternative Minimum Tax from hammering millions of middle-class workers, sources said.

The deal would also extend for one year unemployment insurance benefits set to expire Tuesday, and avert a steep cut to Medicare payments for doctors.

"I can report that we've reached an agreement on the all the tax issues," Senate Minority Leader Mitch McConnell said in an afternoon speech on the Senate floor.

Both sides remained at odds on what to do about the other significant piece of the "fiscal cliff" -- the more than $1 trillion of automatic cuts to defense and domestic programs set to begin Tuesday.

The White House has proposed a three-month delay of the cuts to allow more time to hash out details for deficit reduction, while many Senate Democrats want a flat one-year delay. Republicans insist that some spending cuts should be implemented now as part of any deal.

"In order to get the sequester moved, you're going to have to have real, concrete spending cuts," Rep. Mike Rogers, R-Mich., said. "[Without that], I don't know how it passes the House."

Vice President Joe Biden and McConnell, R-Ky., have been locked in behind-the-scenes negotiations for much of the day, sources said, following several "good" conversations that stretched late into Sunday night.

"We are very, very close," McConnell said Monday. "We can do this. We must do this."

If a deal is reached between Biden and McConnell, members in both chambers would still need to review it and vote on it later today. Passage is far from guaranteed.

"This is one Democrat that doesn't agree with that at all," Iowa Democratic Sen. Tom Harkin said of the tentative deal. "No deal is better than a bad deal, and this looks like a very bad deal the way this is shaping up."

"I don't see how you get something voted on today," Rogers said. "Even if they get a handshake deal today, you have to put the whole thing together and that's probably not going to happen before midnight. So it would make sense to roll into tomorrow to do that."

Failure of Congress to act on a tax measure by Tuesday morning would trigger income tax hikes on all Americans. The average family would pay an extra $3,446 in 2013 under the higher rates, according to the Tax Policy Center.

Regardless of the "cliff," virtually all workers are due to see less in their paychecks starting in January when the temporary 2 percent payroll tax cut will expire. More than $1 trillion in automatic spending cuts to defense and domestic programs will also begin to take effect later this week unless Congress delays or replaces them.

"It is absolutely inexcusable that all of us find ourselves in this place at this time," Sen. Joe Manchin, D-W.Va., said Sunday night on the Senate floor.

"Something has gone terribly wrong when the biggest threat to our American economy is our American Congress," he said, echoing a frustration shared by many Americans.

Both sides say the cost of failure is high.

"If we are not able to reach an agreement, it will be dire," Sen. Jon Kyl, R-Ariz., said Sunday on ABC's "This Week." "Probably at least another million jobs lost, an unemployment rate over 9 percent, and putting us back into recession."